Jet reconstruction and performance using particle flow with the ATLAS Detector

Article

Reference

Jet reconstruction and performance using particle flow with the ATLAS Detector

ATLAS Collaboration

ANCU, Lucian Stefan (Collab.), et al.

Abstract

This paper describes the implementation and performance of a particle flow algorithm applied to 20.2 fb -1 of ATLAS data from 8 TeV proton–proton collisions in Run 1 of the LHC. The algorithm removes calorimeter energy deposits due to charged hadrons from consideration during jet reconstruction, instead using measurements of their momenta from the inner tracker. This improves the accuracy of the charged-hadron measurement, while retaining the calorimeter measurements of neutral-particle energies. The paper places emphasis on how this is achieved, while minimising double-counting of charged-hadron signals between the inner tracker and calorimeter. The performance of particle flow jets, formed from the ensemble of signals from the calorimeter and the inner tracker, is compared to that of jets reconstructed from calorimeter energy deposits alone, demonstrating improvements in resolution and pile-up stability.

ATLAS Collaboration, ANCU, Lucian Stefan (Collab.), et al . Jet reconstruction and performance using particle flow with the ATLAS Detector. The European Physical Journal. C, Particles and Fields , 2017, vol. 77, no. 7, p. 466

DOI : 10.1140/epjc/s10052-017-5031-2

Available at:

http://archive-ouverte.unige.ch/unige:96017

Disclaimer: layout of this document may differ from the published version.

DOI 10.1140/epjc/s10052-017-5031-2 Regular Article - Experimental Physics

Jet reconstruction and performance using particle flow with the ATLAS Detector

ATLAS Collaboration CERN, 1211 Geneva 23, Switzerland

Received: 31 March 2017 / Accepted: 27 June 2017

© CERN for the benefit of the ATLAS collaboration 2017. This article is an open access publication

Abstract This paper describes the implementation and per- formance of a particle flow algorithm applied to 20.2 fb⁻¹of ATLAS data from 8 TeV proton–proton collisions in Run 1 of the LHC. The algorithm removes calorimeter energy deposits due to charged hadrons from consideration dur- ing jet reconstruction, instead using measurements of their momenta from the inner tracker. This improves the accu- racy of the charged-hadron measurement, while retaining the calorimeter measurements of neutral-particle energies. The paper places emphasis on how this is achieved, while min- imising double-counting of charged-hadron signals between the inner tracker and calorimeter. The performance of par- ticle flow jets, formed from the ensemble of signals from the calorimeter and the inner tracker, is compared to that of jets reconstructed from calorimeter energy deposits alone, demonstrating improvements in resolution and pile-up sta- bility.

Contents

1 Introduction . . . . 2 ATLAS detector . . . . 3 Simulated event samples . . . . 3.1 Detector simulation and pile-up modelling . . . 3.2 Truth calorimeter energy and tracking information 4 Data sample . . . . 5 Topological clusters . . . . 6 Particle flow algorithm . . . .

6.1 Containment of showers within a single topo- cluster . . . . 6.2 Track selection . . . . 6.3 Matching tracks to topo-clusters . . . . 6.4 Evaluation of the expected deposited particle

energy through<E_ref^clus/p_ref^trk>determination . 6.4.1 Layer of highest energy density . . . . . 6.5 Recovering split showers . . . . 6.6 Cell-by-cell subtraction . . . . 6.7 Remnant removal . . . .

e-mail:atlas.publications@cern.ch

7 Performance of the subtraction algorithm at truth level 7.1 Track–cluster matching performance . . . . 7.2 Split-shower recovery performance . . . . 7.3 Accuracy of cell subtraction . . . . 7.4 Visualising the subtraction . . . . 8 Jet reconstruction and calibration . . . . 8.1 Overview of particle flow jet calibration . . . . 8.2 Area-based pile-up correction. . . . 8.3 Monte Carlo numerical inversion . . . . 8.4 Global sequential correction . . . . 8.5 In situ validation of JES . . . . 9 Resolution of jets in Monte Carlo simulation. . . . . 9.1 Transverse momentum resolution . . . . 9.2 Angular resolution of jets . . . . 10 Effect of pile-up on the jet resolution and rejection

of pile-up jets . . . . 10.1 Pile-up jet rate . . . . 10.2 Pile-up effects on jet energy resolution . . . . . 11 Comparison of data and Monte Carlo simulation. . . 11.1 Individual jet properties . . . . 11.2 Event-level observables . . . . 12 Conclusions . . . . References. . . .

1 Introduction

Jets are a key element in many analyses of the data collected by the experiments at the Large Hadron Collider (LHC) [1].

The jet calibration procedure should correctly determine the jet energy scale and additionally the best possible energy and angular resolution should be achieved. Good jet reconstruc- tion and calibration facilitates the identification of known resonances that decay to hadronic jets, as well as the search for new particles. A complication, at the high luminosities encountered by the ATLAS detector [2], is that multiple inter- actions can contribute to the detector signals associated with a single bunch-crossing (pile-up). These interactions, which

are mostly soft, have to be separated from the hard interaction that is of interest.

Pile-up contributes to the detector signals from the col- lision environment, and is especially important for higher- intensity operations of the LHC. One contribution arises from particle emissions produced by the additional proton–

proton (pp) collisions occurring in the same bunch crossing as the hard-scatter interaction (in-time pile-up). Further pile- up influences on the signal are from signal remnants in the ATLAS calorimeters from the energy deposits in other bunch crossings (out-of-time pile-up).

In Run 1 of the LHC, the ATLAS experiment used either solely the calorimeter or solely the tracker to reconstruct hadronic jets and soft particle activity. The vast majority of analyses utilised jets that were built from topological clus- ters of calorimeter cells (topo-clusters) [3]. These jets were then calibrated to the particle level using a jet energy scale (JES) correction factor [4–7]. For the final Run 1 jet calibra- tion, this correction factor also took into account the tracks associated with the jet, as this was found to greatly improve the jet resolution [4]. ‘Particle flow’ introduces an alterna- tive approach, in which measurements from both the tracker and the calorimeter are combined to form the signals, which ideally represent individual particles. The energy deposited in the calorimeter by all the charged particles is removed. Jet reconstruction is then performed on an ensemble of ‘particle flow objects’ consisting of the remaining calorimeter energy and tracks which are matched to the hard interaction.

The chief advantages of integrating tracking and calori- metric information into one hadronic reconstruction step are as follows:

• The design of the ATLAS detector [8] specifies a calorimeter energy resolution for single charged pions in the centre of the detector of

σ (E) E = 50%

√E ⊕3.4%⊕ 1%

E , (1)

while the design inverse transverse momentum resolution for the tracker is

σ 1

pT

·pT=0.036%·pT⊕1.3%, (2) where energies and transverse momenta are measured in GeV. Thus for low-energy charged particles, the momen- tum resolution of the tracker is significantly better than the energy resolution of the calorimeter. Furthermore, the acceptance of the detector is extended to softer par- ticles, as tracks are reconstructed for charged particles with a minimum transverse momentum pT>400 MeV, whose energy deposits often do not pass the noise thresh- olds required to seed topo-clusters [9].

• The angular resolution of a single charged particle, recon- structed using the tracker is much better than that of the calorimeter.

• Low-pTcharged particles originating within a hadronic jet are swept out of the jet cone by the magnetic field by the time they reach the calorimeter. By using the track’s azimuthal coordinate¹at the perigee, these particles are clustered into the jet.

• When a track is reconstructed, one can ascertain whether it is associated with a vertex, and if so the vertex from which it originates. Therefore, in the presence of multiple in-time pile-up interactions, the effect of additional parti- cles on the hard-scatter interaction signal can be mitigated by rejecting signals originating from pile-up vertices.² The capabilities of the tracker in reconstructing charged par- ticles are complemented by the calorimeter’s ability to recon- struct both the charged and neutral particles. At high ener- gies, the calorimeter’s energy resolution is superior to the tracker’s momentum resolution. Thus a combination of the two subsystems is preferred for optimal event reconstruc- tion. Outside the geometrical acceptance of the tracker, only the calorimeter information is available. Hence, in the for- ward region the topo-clusters alone are used as inputs to the particle flow jet reconstruction.

However, particle flow introduces a complication. For any particle whose track measurement ought to be used, it is nec- essary to correctly identify its signal in the calorimeter, to avoid double-counting its energy in the reconstruction. In the particle flow algorithm described herein, a Boolean deci- sion is made as to whether to use the tracker or calorime- ter measurement. If a particle’s track measurement is to be used, the corresponding energy must be subtracted from the calorimeter measurement. The ability to accurately subtract all of a single particle’s energy, without removing any energy deposited by any other particle, forms the key performance criterion upon which the algorithm is optimised.

Particle flow algorithms were pioneered in the ALEPH experiment at LEP [10]. They have also been used in the H1 [11], ZEUS [12,13] and DELPHI [14] experiments. Sub- sequently, they were used for the reconstruction of hadronic τ-lepton decays in the CDF [15], D0 [16] and ATLAS [17]

1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and thez-axis along the beam direction. Thex-axis points from the IP to the centre of the LHC ring, and they-axis points upward. Cylindrical coordinates (r, φ)are used in the transverse plane, φ being the azimuthal angle around thez-axis. The pseudorapidity is defined in terms of the polar angleθasη= −ln tan(θ/2). Angular distance is measured in units of

R=

(φ)²+(η)².

2 The standard ATLAS reconstruction defines the hard-scatter primary vertex to be the primary vertex with the largest

p_T²of the associated tracks. All other primary vertices are considered to be contributed by pile-up.

experiments. In the CMS experiment at the LHC, large gains in the performance of the reconstruction of hadronic jets and τ leptons have been seen from the use of particle flow algo- rithms [18–20]. Particle flow is a key ingredient in the design of detectors for the planned International Linear Collider [21]

and the proposed calorimeters are being optimised for its use [22]. While the ATLAS calorimeter already measures jet energies precisely [6], it is desirable to explore the extent to which particle flow is able to further improve the ATLAS hadronic-jet reconstruction, in particular in the presence of pile-up interactions.

This paper is organised as follows. A description of the detector is given in Sect.2, the Monte Carlo (MC) simulated event samples and the dataset used are described in Sects.3 and4, while Sect.5outlines the relevant properties of topo- clusters. The particle flow algorithm is described in Sect.6.

Section7details the algorithm’s performance in energy sub- traction at the level of individual particles in a variety of cases, starting from a single pion through to dijet events. The building and calibration of reconstructed jets is covered in Sect. 8. The improvement in jet energy and angular reso- lution is shown in Sect. 9and the sensitivity to pile-up is detailed in Sect.10. A comparison between data and MC simulation is shown in Sect.11before the conclusions are presented in Sect.12.

2 ATLAS detector

The ATLAS experiment features a multi-purpose detector designed to precisely measure jets, leptons and photons pro- duced in theppcollisions at the LHC. From the inside out, the detector consists of a tracking system called the inner detector (ID), surrounded by electromagnetic (EM) sampling

calorimeters. These are in turn surrounded by hadronic sam- pling calorimeters and an air-core toroid muon spectrometer (MS). A detailed description of the ATLAS detector can be found in Ref. [2].

The high-granularity silicon pixel detector covers the vertex region and typically provides three measurements per track. It is followed by the silicon microstrip tracker which usually provides eight hits, corresponding to four two-dimensional measurement points, per track. These sili- con detectors are complemented by the transition radiation tracker, which enables radially extended track reconstruc- tion up to |η| =2.0. The ID is immersed in a 2 T axial mag- netic field and can reconstruct tracks within the pseudorapid- ity range |η| <2.5. For tracks with transverse momentum pT<100 GeV, the fractional inverse momentum resolution σ (1/pT)·pTmeasured using 2012 data, ranges from approx- imately 2–12% depending on pseudorapidity and pT[23].

The calorimeters provide hermetic azimuthal coverage in the range |η| < 4.9. The detailed structure of the calorimeters within the tracker acceptance strongly influ- ences the development of the shower subtraction algorithm described in this paper. In the central barrel region of the detector, a high-granularity liquid-argon (LAr) electromag- netic calorimeter with lead absorbers is surrounded by a hadronic sampling calorimeter (Tile) with steel absorbers and active scintillator tiles. The same LAr technology is used in the calorimeter endcaps, with fine granularity and lead absorbers for the EM endcap (EMEC), while the hadronic endcap (HEC) utilises copper absorbers with reduced gran- ularity. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules (FCal) optimised for electromagnetic and hadronic measurements respectively. Figure 1 shows the physical location of the different calorimeters. To achieve a high spatial resolution, Fig. 1 Cut-away view of the

ATLAS calorimeter system

Table 1 The granularity inη×φof all the different ATLAS calorimeter layers relevant to the tracking coverage of the inner detector EM LAr calorimeter

Barrel Endcap

Presampler 0.025×π/32 |η|<1.52 0.025×π/32 1.5< |η|<1.8

PreSamplerB/E

1st layer 0.025/8×π/32 |η|<1.4 0.050×π/32 1.375<|η|<1.425

EMB1/EME1 0.025×π/128 1.4< |η|<1.475 0.025×π/32 1.425<|η|<1.5 0.025/8×π/32 1.5< |η|<1.8 0.025/6×π/32 1.8< |η|<2.0 0.025/4×π/32 2.0< |η|<2.4 0.025×π/32 2.4< |η|<2.5 0.1×π/32 2.5< |η|<3.2

2nd layer 0.025×π/128 |η|<1.4 0.050×π/128 1.375<|η|<1.425

EMB2/EME2 0.075×π/128 1.4< |η|<1.475 0.025×π/128 1.425<|η|<2.5 0.1×π/32 2.5< |η|<3.2

3rd layer 0.050×π/128 |η|<1.35 0.050×π/128 1.5< |η|<2.5

EMB3/EME3

Tile calorimeter

Barrel Extended barrel

1st layer 0.1×π/32 |η|<1.0 0.1×π/32 0.8<|η|<1.7

TileBar0/TileExt0

2nd layer 0.1×π/32 |η|<1.0 0.1×π/32 0.8<|η|<1.7

TileBar1/TileExt1

3rd layer 0.2×π/32 |η|<1.0 0.2×π/32 0.8<|η|<1.7

TileBar2/TileExt2

Hadronic LAr calorimeter Endcap

1st layer 0.1×π/32 1.5< |η|<2.5

HEC0 0.2×π/16 2.5< |η|<3.2

2nd layer 0.1×π/32 1.5< |η|<2.5

HEC1 0.2×π/16 2.5<|η|<3.2

3rd layer 0.1×π/32 1.5< |η|<2.5

HEC2 0.2×π/16 2.5<|η|<3.2

4th layer 0.1×π/32 1.5< |η|<2.5

HEC3 0.2×π/16 2.5<|η|<3.2

the calorimeter cells are arranged in a projective geometry with fine segmentation in φ and η. Additionally, each of the calorimeters is longitudinally segmented into multiple layers, capturing the shower development in depth. In the region |η| < 1.8, a presampler detector is used to correct for the energy lost by electrons and photons upstream of the calorimeter. The presampler consists of an active LAr layer of thickness 1.1 cm (0.5 cm) in the barrel (endcap) region. The granularity of all the calorimeter layers within the tracker acceptance is given in Table1.

The EM calorimeter is over 22 radiation lengths in depth, ensuring that there is little leakage of EM showers into

the hadronic calorimeter. The total depth of the complete calorimeter is over 9 interaction lengths in the barrel and over 10 interaction lengths in the endcap, such that good contain- ment of hadronic showers is obtained. Signals in the MS are used to correct the jet energy if the hadronic shower is not completely contained. In both the EM and Tile calorimeters, most of the absorber material is in the second layer. In the hadronic endcap, the material is more evenly spread between the layers.

The muon spectrometer surrounds the calorimeters and is based on three large air-core toroid superconducting magnets with eight coils each. The field integral of the toroids ranges

from 2.0 to 6.0 Tm across most of the detector. It includes a system of precision tracking chambers and fast detectors for triggering.

3 Simulated event samples

A variety of MC samples are used in the optimisation and performance evaluation of the particle flow algorithm. The simplest samples consist of a single charged pion generated with a uniform spectrum in the logarithm of the generated pion energy and in the generatedη. Dijet samples generated withPythia8 (v8.160) [24,25], with parameter values set to the ATLAS AU2 tune [26] and the CT10 parton distribu- tion functions (PDF) set [27], form the main samples used to derive the jet energy scale and determine the jet energy res- olution in simulation. The dijet samples are generated with a series of jetpTthresholds applied to the leading jet, recon- structed from all stable final-state particles excluding muons and neutrinos, using the anti-kt algorithm [28] with radius parameter 0.6 usingFastJet(v3.0.3) [29,30].

For comparison with collision data,Z →μμevents are generated withPowheg- Box(r1556) [31] using the CT10 PDF and are showered withPythia8, with the ATLAS AU2 tune. Additionally, top quark pair production is simulated with MC@NLO (v4.03) [32,33] using the CT10 PDF set, interfaced withHerwig(v6.520) [34] for parton showering, and the underlying event is modelled byJimmy(v4.31) [35].

The top quark samples are normalised using the cross-section calculated at next-to-next-to-leading order (NNLO) in QCD including resummation of next-to-next-to-leading logarith- mic soft gluon terms with top++2.0 [36–43], assuming a top quark mass of 172.5 GeV. Single-top-quark production pro- cesses contributing to the distributions shown are also simu- lated, but their contributions are negligible.

3.1 Detector simulation and pile-up modelling

All samples are simulated using Geant4 [44] within the ATLAS simulation framework [45] and are reconstructed using the noise threshold criteria used in 2012 data-taking [3].

Single-pion samples are simulated without pile-up, while dijet samples are simulated under three conditions: with no pile-up; with pile-up conditions similar to those in the 2012 data; and with a mean number of interactions per bunch cross- ingμ = 40, whereμ follows a Poisson distribution. In 2012, the mean value ofμwas 20.7 and the actual number of interactions per bunch crossing ranged from around 10 to 35 depending on the luminosity. The bunch spacing was 50 ns.

When compared to data, the MC samples are reweighted to have the same distribution ofμas present in the data. In all the samples simulated including pile-up, effects from both the same bunch crossing and previous/subsequent crossings

are simulated by overlaying additional generated minimum- bias events on the hard-scatter event prior to reconstruction.

The minimum-bias samples are generated usingPythia 8 with the ATLAS AM2 tune [46] and the MSTW2009 PDF set [47], and are simulated using the same software as the hard-scatter event.

3.2 Truth calorimeter energy and tracking information For some samples the fullGeant4 hit information [44] is retained for each calorimeter cell such that the true amount of hadronic and electromagnetic energy deposited by each generated particle is known. Only the measurable hadronic and electromagnetic energy deposits are counted, while the energy lost due to nuclear capture and particles escaping from the detector is not included. For a given charged pion the sum of these hits in a given clusterioriginating from this particle is denoted byE_true^clus_{, π}ⁱ .

Reconstructed topo-cluster energy is assigned to a given truth particle according to the proportion ofGeant4hits sup- plied to that topo-cluster by that particle. Using theGeant4 hit information in the inner detector a track is matched to a generated particle based on the fraction of hits on the track which originate from that particle [48].

4 Data sample

Data acquired during the period from March to December 2012 with the LHC operating at a ppcentre-of-mass energy of 8 TeV are used to evaluate the level of agreement between data and Monte Carlo simulation of different outputs of the algorithm. Two samples with a looser preselection of events are reconstructed using the particle flow algorithm. A tighter selection is then used to evaluate its performance.

First, a Z → μμ enhanced sample is extracted from the 2012 dataset by selecting events containing two recon- structed muons [49], each with pT>25 GeV and|η|<2.4, where the invariant mass of the dimuon pair is greater than 55 GeV, and the pT of the dimuon pair is greater than 30 GeV.

Similarly, a sample enhanced in tt¯ → bbq¯ q¯μν events is obtained from events with an isolated muon and at least one hadronic jet which is required to be identified as a jet containing b-hadrons (b-jet). Events are selected that pass single-muon triggers and include one reconstructed muon satisfying pT > 25 GeV, |η| < 2.4, for which the sum of additional track momenta in a cone of size R = 0.2 around the muon track is less than 1.8 GeV. Additionally, a reconstructed calorimeter jet is required to be present with pT >30 GeV, |η|<2.5, and pass the 70% working point of the MV1b-tagging algorithm [50].

For both datasets, all ATLAS subdetectors are required to be operational with good data quality. Each dataset corre- sponds to an integrated luminosity of 20.2 fb⁻¹. To remove events suffering from significant electronic noise issues, cosmic rays or beam background, the analysis excludes events that contain calorimeter jets with pT > 20 GeV which fail to satisfy the ‘looser’ ATLAS jet quality crite- ria [51,52].

5 Topological clusters

The lateral and longitudinal segmentation of the calorimeters permits three-dimensional reconstruction of particle show- ers, implemented in the topological clustering algorithm [3].

Topo-clusters of calorimeter cells are seeded by cells whose absolute energy measurements|E|exceed the expected noise by four times its standard deviation. The expected noise includes both electronic noise and the average contribution from pile-up, which depends on the run conditions. The topo- clusters are then expanded both laterally and longitudinally in two steps, first by iteratively adding all adjacent cells with absolute energies two standard deviations above noise, and finally adding all cells neighbouring the previous set. A split- ting step follows, separating at most two local energy max- ima into separate topo-clusters. Together with the ID tracks, these topo-clusters form the basic inputs to the particle flow algorithm.

The topological clustering algorithm employed in ATLAS is not designed to separate energy deposits from different particles, but rather to separate continuous energy showers of different nature, i.e. electromagnetic and hadronic, and also to suppress noise. The cluster-seeding threshold in the topo-clustering algorithm results in a large fraction of low- energy particles being unable to seed their own clusters. For example, in the central barrel∼25% of 1 GeV charged pions do not seed their own cluster [9].

While the granularity, noise thresholds and employed technologies vary across the different ATLAS calorimeters, they are initially calibrated to the electromagnetic scale (EM scale) to give the same response for electromagnetic show- ers from electrons or photons. Hadronic interactions produce

responses that are lower than the EM scale, by amounts depending on where the showers develop. To account for this, the mean ratio of the energy deposited by a particle to the momentum of the particle is determined based on the position of the particle’s shower in the detector, as described in Sect.6.4.

A local cluster (LC) weighting scheme is used to calibrate hadronic clusters to the correct scale [3]. Further develop- ment is needed to combine this with particle flow; therefore, in this work the topo-clusters used in the particle flow algo- rithm are calibrated at the EM scale.

6 Particle flow algorithm

A cell-based energy subtraction algorithm is employed to remove overlaps between the momentum and energy mea- surements made in the inner detector and calorimeters, respectively. Tracking and calorimetric information is com- bined for the reconstruction of hadronic jets and soft activ- ity (additional hadronic recoil below the threshold used in jet reconstruction) in the event. The reconstruction of the soft activity is important for the calculation of the missing transverse momentum in the event [53], whose magnitude is denoted byE^miss_T .

The particle flow algorithm provides a list of tracks and a list of topo-clusters containing both the unmodified topo- clusters and a set of new topo-clusters resulting from the energy subtraction procedure. This algorithm is sketched in Fig. 2. First, well-measured tracks are selected follow- ing the criteria discussed in Sect.6.2. The algorithm then attempts to match each track to a single topo-cluster in the calorimeter (Sect.6.3). The expected energy in the calorime- ter, deposited by the particle that also created the track, is computed based on the topo-cluster position and the track momentum (Sect. 6.4). It is relatively common for a sin- gle particle to deposit energy in multiple topo-clusters. For each track/topo-cluster system, the algorithm evaluates the probability that the particle energy was deposited in more than one topo-cluster. On this basis it decides if it is nec- essary to add more topo-clusters to the track/topo-cluster system to recover the full shower energy (Sect. 6.5). The

Fig. 2 A flow chart of how the particle flow algorithm proceeds, start- ing with track selection and continuing until the energy associated with the selected tracks has been removed from the calorimeter. At the end,

charged particles, topo-clusters which have not been modified by the algorithm, and remnants of topo-clusters which have had part of their energy removed remain

expected energy deposited in the calorimeter by the particle that produced the track is subtracted cell by cell from the set of matched topo-clusters (Sect.6.6). Finally, if the remaining energy in the system is consistent with the expected shower fluctuations of a single particle’s signal, the topo-cluster rem- nants are removed (Sect.6.7).

This procedure is applied to tracks sorted in descending pT-order, firstly to the cases where only a single topo-cluster is matched to the track, and then to the other selected tracks.

This methodology is illustrated in Fig.3.

Details about each step of the procedure are given in the rest of this section. After some general discussion of the prop- erties of topo-clusters in the calorimeter, the energy sub- traction procedure for each track is described. The proce- dure is accompanied by illustrations of performance metrics used to validate the configuration of the algorithm. The sam- ples used for the validation are single-pion and dijet MC samples without pile-up, as described in the previous sec- tion. Charged pions dominate the charged component of the jet, which on average makes up two-thirds of the vis- ible jet energy [54,55]. Another quarter of the jet energy is contributed by photons from neutral hadron decays, and the remainder is carried by neutral hadrons that reach the calorimeter. Because the majority of tracks are generated by charged pions [56], particularly at low pT, the pion mass hypothesis is assumed for all tracks used by the particle flow algorithm to reconstruct jets. Likewise the energy sub- traction is based on the calorimeter’s response to charged pions.

In the following sections, the values for the parameter set and the performance obtained for the 2012 dataset are discussed. These parameter values are not necessarily the product of a full optimisation, but it has been checked that the performance is not easily improved by variations of these choices. Details of the optimisation are beyond the scope of the paper.

6.1 Containment of showers within a single topo-cluster The performance of the particle flow algorithm, especially the shower subtraction procedure, strongly relies on the topological clustering algorithm. Hence, it is important to quantify the extent to which the clustering algorithm dis- tinguishes individual particles’ showers and how often it splits a single particle’s shower into more than one topo- cluster. The different configurations of topo-clusters contain- ing energy from a given single pion are classified using two variables.

For a given topo-clusteri, the fraction of the particle’s true energy contained in the topo-cluster (see Sect.3.2), with respect to the total true energy deposited by the particle in all clustered cells, is defined as

ε^clus_i = E_true^clus_{, π}ⁱ

E_true^{all topo}_{, π}^−clusters, (3)

whereE_true^clus_{, π}ⁱ is the true energy deposited in topo-clusteriby the generated particle under consideration andE^{all topo}_{true, π}^−clusters is the true energy deposited in all topo-clusters by that truth particle. For each particle, the topo-cluster with the highest value ofε_i^clusis designated the leading topo-cluster, for which ε^clus_lead=ε^clus_i . The minimum number of topo-clusters needed to capture at least 90% of the particle’s true energy, i.e. such that_n

i=0ε^clus_i >90%, is denoted byn⁹⁰_clus.

Topo-clusters can contain contributions from multiple par- ticles, affecting the ability of the subtraction algorithm to separate the energy deposits of different particles. The purity ρ_i^clus for a topo-clusteri is defined as the fraction of true energy within the topo-cluster which originates from the par- ticle of interest:

ρi^clus= E_true^clus_{, π}ⁱ E_true^clus_,ⁱall particles

. (4)

For the leading topo-cluster, defined by having the highest ε^clus_i , the purity value is denoted byρ_lead^clus.

Only charged particles depositing significant energy (at least 20% of their true energy) in clustered cells are consid- ered in the following plots, as in these cases there is signifi- cant energy in the calorimeter to remove. This also avoids the case where insufficient energy is present in any cell to form a cluster, which happens frequently for very low-energy par- ticles [3].

Figure 3 illustrates how the subtraction procedure is designed to deal with cases of different complexity. Four dif- ferent scenarios are shown covering cases where the charged pion deposits its energy in one cluster, in two clusters, and where there is a nearby neutral pion which either deposits its energy in a separate cluster or the same cluster as the charged pion.

Several distributions are plotted for the dijet sample in which the energy of the leading jet, measured at truth level, is in the range 20 < p^lead_T <500 GeV. The distribution of ε^clus_lead is shown in Fig. 4 for different p_T^true andη^true bins.

It can be seen thatε^clus_leaddecreases as the pTof the particle increases and very little dependence onηis observed. Figure 5shows the distribution ofn⁹⁰_clus. As expected,n⁹⁰_clusincreases with particle pT. It is particularly interesting to know the fraction of particles for which at least 90% of the true energy is contained in a single topo-cluster (n⁹⁰_clus = 1) and this is shown in Fig.6. Lastly, Fig.7shows the distribution ofρ_lead^clus. This decreases as p_T^trueincreases and has little dependence on|η^true|.

For more than 60% of particles with 1<p^true_T <2 GeV, the shower is entirely contained within a single topo-cluster

Fig. 3 Idealised examples of how the algorithm is designed to deal with several different cases. Theredcells are those which have energy from theπ⁺, thegreencells energy from the photons from theπ⁰ decay, thedotted linesrepresent the original topo-cluster boundaries with those outlined inbluehaving been matched by the algorithm to

theπ⁺, while those in black are yet to be selected. The different layers in the electromagnetic calorimeter (Presampler, EMB1, EMB2, EMB3) are indicated. In this sketch only the first two layers of the Tile calorime- ter are shown (TileBar0 and TileBar1)

(a) (b) (c)

Fig. 4 Distribution of the fraction of the total true energy in the leading topo-cluster,ε^cluslead, for charged pions which deposit significant energy (20% of the particle’s energy) in the clustered cells for three different p_T^truebins in three|η^true|regions. The data are taken from a dijet sample

without pile-up with 20<p^lead_T <500 GeV and the statistical uncer- tainties on the number of MC simulated events are shown as ahatched band

(a) (b) (c)

Fig. 5 Distributions of the number of topo-clusters required to con- tain>90% of the true deposited energy of a single charged pion which deposits significant energy (20% of the particle’s energy) in the clus- tered cells. The distributions are shown for three p^true_T bins in three

|η^true|regions. The data are taken from a dijet sample without pile-up with 20 < p^lead_T < 500 GeV and the statistical uncertainties on the number of MC simulated events are shown as ahatched band

(ε_lead^clus∼1). This fraction falls rapidly with particlepT, reach- ing∼25% for particles in the range 5< p_T^true<10 GeV. For particles with p_T^true<2 GeV, 90% of the particle energy can be captured within two topo-clusters in∼95% of cases. The topo-cluster purity also falls as the pion pTincreases, with the target particle only contributing between 38 and 45% of the topo-cluster energy when 5<p^true_T <10 GeV. This is in part due to the tendency for high-pTparticles to be produced in dense jets, while softer particles from the underlying event tend to be isolated from nearby activity.

In general, the subtraction of the hadronic shower is easier for cases with topo-clusters with highρ_i^clus, and highε_i^clus, since in this configuration the topo-clustering algorithm has separated out the contributions from different particles.

6.2 Track selection

Tracks are selected which pass stringent quality criteria: at least nine hits in the silicon detectors are required, and tracks

must have no missing Pixel hits when such hits would be expected [57]. This selection is designed such that the num- ber of badly measured tracks is minimised and is referred to as ‘tight selection’. No selection cuts are made on the association to the hard scatter vertex at this stage Addition- ally, tracks are required to be within |η| < 2.5 and have pT > 0.5 GeV. These criteria remain efficient for tracks from particles which are expected to deposit energy below the threshold needed to seed a topo-cluster or particles that do not reach the calorimeter. Including additional tracks by reducing the pTrequirement to 0.4 GeV leads to a substan- tial increase in computing time without any corresponding improvement in jet resolution. This is due to their small con- tribution to the total jetpT.

Tracks with pT >40 GeV are excluded from the algo- rithm, as such energetic particles are often poorly isolated from nearby activity, compromising the accurate removal of the calorimeter energy associated with the track. In such cases, with the current subtraction scheme, there is no advan-

[GeV]

true

pT

5 10 15 20 25 30 35 40

=1) clus90 Probability (n

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ATLAS Simulation

s=8TeV 0.0<|η^true|<1.0

|<2.0 ηtrue

1.0<|

|<2.5 ηtrue

2.0<|

Fig. 6 The probability that a single topo-cluster contains> 90% of the true deposited energy of a single charged pion, which deposits sig- nificant energy (20% of the particle’s energy) in the clustered cells.

The distributions are shown as a function of p_T^true in three |η^true| regions. The data are taken from a dijet sample without pile-up with 20< p^lead_T <500 GeV and the statistical uncertainties on the number of MC simulated events are shown as ahatched band

tage in using the tracker measurement. This requirement was tuned both by monitoring the effectiveness of the energy sub- traction using the true energy deposited in dijet MC events, and by measuring the jet resolution in MC simulation. The majority of tracks in jets with pT between 40 and 60 GeV havepTbelow 40 GeV, as shown later in Sect.11.

In addition, any tracks matched to candidate electrons [58]

or muons [49], without any isolation requirements, identified with medium quality criteria, are not selected and therefore are not considered for subtraction, as the algorithm is opti- mised for the subtraction of hadronic showers. The energy deposited in the calorimeter by electrons and muons is hence

taken into account in the particle flow algorithm and any resulting topo-clusters are generally left unsubtracted.

Figure8shows the charged-pion track reconstruction effi- ciency, for the tracks selected with the criteria described above, as a function ofη^trueand p_T^truein the dijet MC sample, with leading jets in the range 20 < p^lead_T <1000 GeV and with similar pile-up to that in the 2012 data. The Monte Carlo generator information is used to match the reconstructed tracks to the generated particles [48]. The application of the tight quality criteria substantially reduces the rate of poorly measured tracks, as shown in Fig.9. Additionally, using the above selection, the fraction of combinatorial fake tracks arising from combining ID hits from different particles is negligible [48].

6.3 Matching tracks to topo-clusters

To remove the calorimeter energy where a particle has formed a single topo-cluster, the algorithm first attempts to match each selected track to one topo-cluster. The distancesφand ηbetween the barycentre of the topo-cluster and the track, extrapolated to the second layer of the EM calorimeter, are computed for each topo-cluster. The topo-clusters are ranked based on the distance metric

R=

φ σ_φ

2

+ η

σ_η 2

, (5)

whereσ_ηandσ_φ represent the angular topo-cluster widths, computed as the standard deviation of the displacements of the topo-cluster’s constituent cells inη andφ with respect to the topo-cluster barycentre. This accounts for the spa- tial extent of the topo-clusters, which may contain energy deposits from multiple particles.

The distributions ofσ_ηandσ_φfor single-particle samples are shown in Fig.10. The structure seen in these distribu-

(a) (b) (c)

Fig. 7 The purityρlead^clus, defined for a selected charged pion as the frac- tional contribution of the chosen particle to the total true energy in the leading topo-cluster, shown for pions withε^cluslead>50%. Distributions are shown for several p_T^truebins and in three|η^true|regions. The data are

taken from a dijet sample without pile-up with 20<p^lead_T <500 GeV and the statistical uncertainties on the number of MC simulated events are shown as ahatched band

ηtrue

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Track Reconstruction Efficiency

0.65 0.7 0.75 0.8 0.85 0.9

0.95 ATLAS Simulation s=8TeV

< 2 GeV

true

1 < pT

< 5 GeV

true

2 < pT

< 10 GeV

true

5 < pT

(a)

[GeV]

true

pT

1 10

Track Reconstruction Efficiency

0.65 0.7 0.75 0.8 0.85 0.9

0.95 ATLAS Simulation s=8TeV

|<1.0 ηtrue

|

|<2.0 ηtrue

1.0<|

|<2.5 ηtrue

2.0<|

(b)

Fig. 8 The track reconstruction efficiency for charged pions after applying the tight quality selection criteria to the tracks. Subfigure (a) shows the efficiency for 1–2 GeV, 2–5 GeV and 5–10 GeV parti- cles as a function ofη, while (b) shows the track reconstruction effi-

ciency as a function ofp_Tin three |η|bins. A simulated dijet sample is used, with similar pile-up to that in the 2012 data, and for which 20<p^lead_T <1000 GeV. The statistical uncertainties in the number of MC simulated events are shown in adarker shading

[GeV]

true

-pT trk

pT

-10 -8 -6 -4 -2 0 2 4 6 8 10

-1 Tracks / 400 MeV / nb

10-1

1 10 102

103

104

105

106 1 < p^true_T < 2 GeV

|<1.0 ηtrue

|

= 8 TeV ATLAS Simulation s

Nominal reconstruction After hit requirements

< p^true_T <2 GeV,

|η^true|<1.0.

[GeV]

true

-pT trk

pT

-10 -8 -6 -4 -2 0 2 4 6 8 10

-1 Tracks / 400 MeV / nb

10-1

1 10 102

103

104 5 < p^true_T < 10 GeV

|<2.5 ηtrue

2.0<|

= 8 TeV ATLAS Simulation s

Nominal reconstruction After hit requirements

(a)1 (b)5< p^true_T <10 GeV,

2.0<|η^true|<2.5.

Fig. 9 The difference between the reconstructedp_Tof the track from a charged pion and the particle’s truep_Tfor two bins in truth particlep_T and|η|, determined in dijet MC simulation with similar pile-up to that in the 2012 data. Theshaded bandsrepresent the statistical uncertainty.

The tails in the residuals are substantially diminished upon the applica-

tion of the more stringent silicon detector hit requirements. A simulated dijet sample with 20< p^lead_T <1000 GeV is used, and the statistical uncertainties in the number of MC simulated events are shown as a hatched band

tions is related to the calorimeter geometry. Each calorime- ter layer has a different cell granularity in both dimensions, and this sets the minimum topo-cluster size. In particular, the granularity is significantly finer in the electromagnetic calorimeter, thus particles that primarily deposit their energy in either the electromagnetic and hadronic calorimeters form distinct populations. High-energy showers typically spread over more cells, broadening the corresponding topo-clusters.

If the computed value ofσ_ηorσ_φis smaller than 0.05, it is set to 0.05.

A preliminary selection of topo-clusters to be matched to the tracks is performed by requiring thatE^clus/p^trk >0.1,

where E^clus is the energy of the topo-cluster and p^trkis the track momentum. The distribution ofE^clus/p^trkfor the topo- cluster with at least 90% of the true energy from the particle matched to the track – the “correct” one to match to – and for the closest other topo-cluster inRis shown in Fig.11. For very soft particles, it is common that the closest other topo- cluster carries E^clus/p^trk comparable to (although smaller than) the correct topo-cluster. About 10% of incorrect topo- clusters are rejected by theE^clus/p^trk cut for particles with 1 < pT < 2 GeV. The difference in E^clus/p^trk becomes much more pronounced for particles with pT > 5 GeV, for which there is a very clear separation between the cor-

(a) (b) (c)

(d) (e) (f)

Fig. 10 The distribution ofσηandσφ, for charged pions, in three dif- ferent regions of the detector for three particlep_Tranges. The data are taken from a dijet sample without pile-up with 20<p^lead_T <500 GeV

and the statistical uncertainties on the number of MC simulated events are shown as ahatched band

rect and incorrect topo-cluster matches, resulting in a 30–

40% rejection rate for the incorrect topo-clusters. This is because at lower pTclusters come from both signal and elec- tronic or pile-up noise. Furthermore, the particle pT spec- trum is peaked towards lower values, and thus higher-pT

topo-clusters are rarer. The E^clus/p^trk > 0.1 requirement rejects the correct cluster for far less than 1% of particles.

Next, an attempt is made to match the track to one of the preselected topo-clusters using the distance metricR defined in Eq.5. The distribution ofRbetween the track and the topo-cluster with>90% of the truth particle energy and to the closest other preselected topo-cluster is shown in Fig.12for the dijet MC sample. From this figure, it is seen that the correct topo-cluster almost always lies at a smallRrelative to other clusters. Hence, the closest pres- elected topo-cluster inRis taken to be the matched topo- cluster. This criterion selects the correct topo-cluster with a high probability, succeeding for virtually all particles with pT > 5 GeV. If no preselected topo-cluster is found in a cone of sizeR=1.64, it is assumed that this particle did not form a topo-cluster in the calorimeter. In such cases the track is retained in the list of tracks and no subtraction is performed. The numerical value corresponds to a one-sided Gaussian confidence interval of 95%, and has not been opti- mised. However, as seen in Fig.12, this cone size almost

always includes the correct topo-cluster, while rejecting the bulk of incorrect clusters.

6.4 Evaluation of the expected deposited particle energy throughE_ref^clus/p_ref^trkdetermination

It is necessary to know how much energy a particle with measured momentum p^trk deposits on average, given by Edep = p^trkE^clus_ref /p^trk_ref, in order to correctly subtract the energy from the calorimeter for a particle whose track has been reconstructed. The expectation valueE^clus_ref /p^trk_ref (which is also a measure of the mean response) is determined using single-particle samples without pile-up by summing the energies of topo-clusters in aRcone of size 0.4 around the track position, extrapolated to the second layer of the EM calorimeter. This cone size is large enough to entirely capture the energy of the majority of particle showers. This is also sufficient in dijet events, as demonstrated in Fig.13, where one might expect the clusters to be broader due to the pres- ence of other particles. The subscript ‘ref’ is used here and in the following to indicateE^clus/p^trkvalues determined from single-pion samples.

Variations in E_ref^clus/p_ref^trk due to detector geometry and shower development are captured by binning the measure- ment in the pT andη of the track as well as the layer of

(a) (b) (c)

(d) (e) (f)

Fig. 11 The distributions ofE^clus/p^trk for the topo-cluster with>

90% of the true energy of the particle and the closest other topo-cluster inR. The data are taken from a dijet sample without pile-up with 20< p^lead_T <500 GeV and the statistical uncertainties on the number

of MC simulated events are shown as ahatched band. A track is only used for energy subtraction if a topo-cluster is found inside a cone of R=1.64 for whichE^clus/p^trk >0.1, as indicated by thevertical dashed line

highest energy density (LHED), defined in the next section.

The LHED is also used to determine the order in which cells are subtracted in subsequent stages of the algorithm.

The spread of the expected energy deposition, denoted by σ (Edep), is determined from the standard deviation of the E_ref^clus/p_ref^trkdistribution in single-pion samples. It is used in order to quantify the consistency of the measuredE^clus/p^trk with the expectation from E_ref^clus/p_ref^trk in both the split- shower recovery (Sect.6.5) and remnant removal (Sect.6.7).

6.4.1 Layer of highest energy density

The dense electromagnetic shower core has a well-defined ellipsoidal shape inη–φ. It is therefore desirable to locate this core, such that the energy subtraction may be performed first in this region before progressing to the less regular shower periphery. The LHED is taken to be the layer which shows the largest rate of increase in energy density, as a function of the number of interaction lengths from the front face of the calorimeter. This is determined as follows:

• The energy density is calculated for the jth cell in theith layer of the calorimeter as

ρi j = Ei j

Vi j

GeV/X₀³

, (6)

withEi jbeing the energy in andVi jthe volume of the cell expressed in radiation lengths. The energy measured in the Presampler is added to that of the first layer in the EM calorimeter. In addition, the Tile and HEC calorimeters are treated as single layers. Thus, the procedure takes into account four layers – three in the EM calorimeter and one in the hadronic calorimeter. Only cells in the topo-clusters matched to the track under consideration are used.

• Cells are then weighted based on their proximity to the extrapolated track position in the layer, favouring cells that are closer to the track and hence more likely to con- tain energy from the selected particle. The weight for each cell, wi j, is computed from the integral over the cell area inη–φof a Gaussian distribution centred on the extrapolated track position with a width inRof 0.035, similar to the Molière radius of the LAr calorimeter.

• A weighted average energy density for each layer is cal- culated as